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and chromatic tune spread. Here, the first-turn losses due
to injection and H- stripping are omitted from the loss
curve. For high beam intensities the tune are effectively
depressed by the space charge. The only resonances up to
the 4th order, which beam crosses during accumulation,
are the difference resonances. As a result of the space
charge coupling, the beam with approximately similar
transverse beam emittances is not susceptible to the
difference resonance. The intensity limitation for this
working point is associated with the coherent beam
response near the tune of 6.0, which limits beam intensity
to slightly above N=2* 1014 at the energy of 1 GeV [10].
However, this limitation is due to the structure resonances
and thus is very strict.6.25
G~6.2
6.15
~.6.16.051
2'
6.05 6.1 6.15 6.2 625
horizontal tuneThe losses due to these resonance are very strong,
however, they are all imperfection resonances. With an
appropriate correction schemes, which are available in the
SNS, one can attempt to compensate such resonances. As
a result, with successful compensation, the real loss for
this working point happens only at a very high intensity
due to the coherent beam response to the structure
resonances, as shown in Fig. 6.6.8
6.6
6.4
6.26 6.2 6.4 6.6 6.8 7
Figure 5: Tune space for working point (6.4,6.3), with 2nd
order resonances shown in red, 3rd order structure
resonance shown in green, and the imperfection
resonances shown in black. The tune spread for a 2MW
beam is shown for dp/p=0, 0.7 and 1% with green, red
and pink colors, respectively.7
Figure 3: Tune spread for three beam intensities
At the end of accumulation: N=0.l* 1014 (red),
N=1.0*1014 (pink) and N=2.0* 1014 (green).3
2.52
0
1.5
10.5
1 1.5 2 2.
Number of protons * 10^146
5
23
Figure 4: Loss curve for the working point (6.23,6.20).
For the working point (6.4,6.3), the loss curve
demonstrates impact of each individual resonance crossed
during accumulation. The strong loss at low intensity is
due to the sum sextupole resonance at which the working
point is located so that for real operation the tunes should
be slightly adjusted to avoid this strong resonance loss.
Other loss peaks are due to the 3rd and 4th order
resonances which are crossed for higher beam intensity.2 3 4
Number ofprotonis*1014Figure 6: Loss curve for the working point (6.4,6.3).
5 REFERENCES
[1] N.Malitsky and R.Tahnan, AIP 391 (1996).
[2] N. Malitsky and R.Talman, ICAP 98 (1998).
[3] A.V. Fedotov et al., Proc. of EPAC'00, p.1492.
[4] I. Papaphilippou, Proc. of PAC'01 (Chicago), p.462.
[5] A.V. Fedotov et al., Proc. of PAC'O1, p. 2851.
[6] A.V. Fedotov, SNS project ASAC reviews (2001-02).
[7] A.V. Fedotov et al., Proc. of PAC'01, p. 2848.
[8] A.V. Fedotov, N. Malistky and J. Wei, BNL/SNS
Tech. Note 086 (2001).
[9] A.V. Fedotov et al., "Exploring transverse beam
stability in the SNS in the presence of space charge",
these Proceeding.
[10] A.V. Fedotov and I.Hofmann, "Half Intger resonance
crossing and space charge limit", these Proceedings7
4
L J.
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Malitsky, N.; Fedotov, A. V. & Wei, J. Application of UAL to High Intensity Beam Dynamics Studies in the SNS Accumulator Ring, article, June 3, 2002; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc742625/m1/3/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.